Methods of Applied Mathematics (eBook)

Francis B. Hildebrand (Autor)

eBook Download: EPUB

2012
362 Seiten
Dover Publications (Verlag)
978-0-486-13838-1 (ISBN)

Infos

Offering a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, this book explores linear algebraic equations, quadratic and Hermitian forms, the calculus of variations, more.

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This invaluable book offers engineers and physicists working knowledge of a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, but nevertheless extremely useful when applied to typical problems in many different fields. It deals principally with linear algebraic equations, quadratic and Hermitian forms, operations with vectors and matrices, the calculus of variations, and the formulations and theory of linear integral equations. Annotated problems and exercises accompany each chapter.

Inhalt

CHAPTER ONE Matrices and Linear Equations1.1. Introduction1.2. Linear equations. The Gauss-Jordan reduction1.3. Matrices1.4. Determinants. Cramer's rule1.5. Special matrices1.6. The inverse matrix1.7. Rank of a matrix1.8. Elementary operations1.9. Solvability of sets of linear equations1.10. Linear vector space1.11. Linear equations and vector space1.12. Characteristic-value problems1.13. Orthogonalization of vector sets1.14. Quadratic forms1.15. A numerical example1.16. Equivalent matrices and transformations1.17. Hermitian matrices1.18. Multiple characteristic numbers of symmetric matrices1.19. Definite forms1.20. Discriminants and invariants1.21. Coordinate transformations1.22. Functions of symmetric matrices1.23. Numerical solution of characteristic-value problems1.24. Additional techniques1.25. Generalized characteristic-value problems1.26. Characteristic numbers of nonsymmetric matrices1.27. A physical application1.28. Function space1.29. Sturm-Liouville problems References ProblemsCHAPTER TWO Calculus of Variations and Applications2.1. Maxima and minima2.2. The simplest case2.3. Illustrative examples2.4. Natural boundary conditions and transition conditions2.5. The variational notation2.6. The more general case2.7. Constraints and Lagrange multipliers2.8. Variable end points2.9. Sturm-Liouville problems2.10. Hamilton's principle2.11. Lagrange's equations2.12. Generalized dynamical entities2.13. Constraints in dynamical systems2.14. Small vibrations about equilibrium. Normal coordinates2.15. Numerical example2.16. Variational problems for deformable bodies2.17. Useful transformations2.18. The variational problem for the elastic plate2.19. The Rayleigh-Ritz method2.20 A semidirect method References ProblemsCHAPTER THREE Integral Equations3.1. Introduction3.2. Relations between differential and integral equations3.3. The Green's function3.4. Alternative definition of the Green's function3.5. Linear equations in cause and effect. The influence function3.6. Fredholm equations with separable kernels3.7. Illustrative example3.8. Hilbert-Schmidt theory3.9. Iterative methods for solving equations of the second kind3.10. The Neumann series3.11. Fredholm theory3.12. Singular integral equations3.13. Special devices3.14. Iterative approximations to characteristic functions3.15. Approximation of Fredholm equations by sets of algebraic equations3.16. Approximate methods of undetermined coefficients3.17. The method of collocation3.18. The method of weighting functions3.19. The method of least squares3.20. Approximation of the kernel References ProblemsAPPENDIX The Crout Method for Solving Sets of Linear Algebraic EquationsA. The procedureB. A numerical exampleC. Application to tridiagonal systemAnswers to ProblemsIndex

Produkt-Details

• Erscheint lt. Verlag: 8.6.2012
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 140 x 140 mm
• Gewicht: 390 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• ISBN-10: 0-486-13838-0 / 0486138380
• ISBN-13: 978-0-486-13838-1 / 9780486138381